A Mathematical Model of a Vibrating Soil-Foundation System

Abstract

The displacement amplitudes and the phase angles of vertically vibrating rigid circular plates on an elastic isotropic homogeneous half‐space have been expressed in terms of the mass of the plate, the static spring constant multiplied by a frequency‐dependent function, and a damping term. The results have been modified to apply to vibrating soil‐foundation systems. The effects of hysteresis damping, nonlinear load‐deflection characteristics of soils, the static prepressure, the change of soil properties with depth, and the difference between static and dynamic stress‐strain relations of soils have been considered. The mathematical model has been compared with data on vibrations of circular foundations. The agreement between the model and the experimental data for cohesive soils is very good.

Lumped parameter model for vertical vibrations of surface circular foundations on nonhomogeneous soil

“…That simplified proposed LPM is a marvel of simplicity. In the years after that, the idea of the LPM has attracted many investigators such as Lysmer and Richart (1966), Weissmann (1966), Whitman and Richart (1967), Hall (1967), Veletsos and Wei (1971), Roesset et al (1973) and Veletsos (1975). Recently, Zahafi and Hadid (2019) proposed a newly frequency-independent simplified LPM to simulate circular foundations resting on homogeneous elastic half-space and undergoing vertical vibrations.…”

Simplified frequency-independent model for vertical vibrations of surface circular foundations

“…After the Hsieh (1962) approach, Lysmer (1965) provided frequency-independent dynamic parameters for stiffness and damping constants, which are a marvel of simplicity. The idea of developing a lumped-parameter model comprised mass-spring-dashpot for a rigid mass on the surface of a half-space attracted many investigators such as Lysmer and Richart (1966), Weissmann (1966), Whitman and Richart (1967), Hall (1967), Veletsos and Wei (1971), Roesset et al (1973) and Veletsos (1975). In addition, various studies (Veletsos and Nair, 1974a, 1974b; Meek and Wolf, 1992; Meek and Wolf, 1993; Pradhan et al , 2004) developed a cone model to simulate the unbounded soil for foundation vibration analysis.…”